where \({x_p}\)  is the input radiated symbol and \({x_{{p_1}}}\)  is the demodulated output radiated symbol, \(\mathbb {D}({x_p},{x_{{p_1}}})\)  is the Hamming distance between \({x_p}\)  and \({x_{{p_1}}}\) , \(\mathbb {Q}\left( \cdot \right)\)  is the Q-function [1]}, \(\left| {{x_p},{x_{{p_1}}}} \right| = 2\mathbb {R}\left[ {{x_p}{{\left( {{x_p} - {x_{{p_1}}}} \right)}^ * }} \right]\)  is the codeword difference between \({x_p}\)  and \({x_{{p_1}}}\) . Furthermore, the conditional correct estimation probability of bits conveyed by the radiated symbol is derived by
\(\mathcal {P}\left( {{\Delta _{{\text{mod}}}}\left| {{\Delta _{{\text{ant}}}}{\Delta _{{\text{OAM}}}}} \right.} \right) = 1 - e_{{\text{mod}}}^{\text{b}}.\qquad \mathrm {(39)}\) 
